Abstract We prove a compactness result in GBD {\operatorname{GBD}} which also provides new proof of the theorem GSBD {\operatorname{GSBD}} , due to Chambolle and Crismale. Our is based on Fréchet–Kolmogorov criterion does not rely Korn or Poincaré–Korn inequalities.

We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-orde...

The purpose of this paper is to construct the concept of semi$theta$-compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$-compactness and locally semi -compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.

In this paper, the theory of Oθ-convergence and weak Oθ-convergence of nets is introduced in L-spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shi’s O-convergence. It can be used to characterize preclosed sets, preopen sets, θ-closed sets, θ-open sets, almost F -compactness and almost S-compactness.

‎‎The investigation of equational compactness was initiated by‎ ‎Banaschewski and Nelson‎. ‎They proved that pure injectivity is‎ ‎equivalent to equational compactness‎. ‎Here we define the so‎ ‎called sequentially compact acts over semigroups and study‎ ‎some of their categorical and homological properties‎. ‎Some‎ ‎Baer conditions for injectivity of S-acts are also presented‎.

in this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.

A compactness criterion for Stieltjes transformation S λ : L 2 → L 2 of the form (1.1) is obtained. The main result is conditions for belonging S λ to Schatten-von Neumann class S p , 0 < p < ∞.

In this paper we consider a dominating Finsler metric on a complete Riemannian manifold. First we prove that the energy integral of the Finsler metric satisfies the Palais-Smale condition, and ask for the number of geodesics with endpoints in two given submanifolds. Using Lusternik-Schnirelman theory of critical points we obtain some multiplicity results for the number of Finsler-geodesics betw...

Given a manifold M and a proper sub-bundle ∆ ⊂ TM , we study homotopy properties of the horizontal base-point free loop space Λ, i.e. the space of absolutely continuous maps γ : S → M whose velocities are constrained to ∆ (for example: legendrian knots in a contact manifold). A key technical ingredient for our study is the proof that the base-point map F : Λ → M (the map associating to every lo...

in this paper, using pre-semi-open l-sets and their inequality, a new notion of ps-compactness is introduced in l-topological spaces, where l is a complete de morgan algebra. this notion does not depend on the structure of the basis lattice l and l does not need any distributivity.